Theorem bj-peircei 37190

Description: Inference associated with peirce 205. (Contributed by BJ, 30-Mar-2020.)

Hypothesis

Ref	Expression
bj-peircei.1	⊢ ((𝜑 → 𝜓) → 𝜑)

Assertion

Ref	Expression
bj-peircei	⊢ 𝜑

Proof of Theorem bj-peircei

Step	Hyp	Ref	Expression
1		bj-peircei.1	. 2 ⊢ ((𝜑 → 𝜓) → 𝜑)
2		peirce 205	. 2 ⊢ (((𝜑 → 𝜓) → 𝜑) → 𝜑)
3	1, 2	ax-mp 5	1 ⊢ 𝜑

This proof depends on syntax axioms:   → wi 4

This proof depends on axioms:  ax-mp 5  ax-1 6  ax-2 7  ax-3 8

This theorem is used by: (None)